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• W3217791106 endingPage "2053" @default.
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• W3217791106 abstract "<p style='text-indent:20px;'>Let <inline-formula><tex-math id=M1>begin{document}$ mathit{boldsymbol{mathrm{G}}} $end{document}</tex-math></inline-formula> be a semisimple linear algebraic group defined over rational numbers, <inline-formula><tex-math id=M2>begin{document}$ mathrm{K} $end{document}</tex-math></inline-formula> be a maximal compact subgroup of its real points and <inline-formula><tex-math id=M3>begin{document}$ Gamma $end{document}</tex-math></inline-formula> be an arithmetic lattice. One can associate a probability measure <inline-formula><tex-math id=M4>begin{document}$ mu_{ mathrm{H}} $end{document}</tex-math></inline-formula> on <inline-formula><tex-math id=M5>begin{document}$ Gamma backslash mathrm{G} $end{document}</tex-math></inline-formula> for each subgroup <inline-formula><tex-math id=M6>begin{document}$ mathit{boldsymbol{mathrm{H}}} $end{document}</tex-math></inline-formula> of <inline-formula><tex-math id=M7>begin{document}$ mathit{boldsymbol{mathrm{G}}} $end{document}</tex-math></inline-formula> defined over <inline-formula><tex-math id=M8>begin{document}$ mathbb{Q} $end{document}</tex-math></inline-formula> with no non-trivial rational characters. As G acts on <inline-formula><tex-math id=M9>begin{document}$ Gamma backslash mathrm{G} $end{document}</tex-math></inline-formula> from the right, we can push forward this measure by elements from <inline-formula><tex-math id=M10>begin{document}$ mathrm{G} $end{document}</tex-math></inline-formula>. By pushing down these measures to <inline-formula><tex-math id=M11>begin{document}$ Gamma backslash mathrm{G}/ mathrm{K} $end{document}</tex-math></inline-formula>, we call them homogeneous. It is a natural question to ask what are the possible weak-<inline-formula><tex-math id=M12>begin{document}$ * $end{document}</tex-math></inline-formula> limits of homogeneous measures. In the non-divergent case this has been answered by Eskin–Mozes–Shah. In the divergent case Daw–Gorodnik–Ullmo prove a refined version in some non-trivial compactifications of <inline-formula><tex-math id=M13>begin{document}$ Gamma backslash mathrm{G}/ mathrm{K} $end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=M14>begin{document}$ mathit{boldsymbol{mathrm{H}}} $end{document}</tex-math></inline-formula> generated by real unipotents. In the present article we build on their work and generalize the theorem to the case of general <inline-formula><tex-math id=M15>begin{document}$ mathit{boldsymbol{mathrm{H}}} $end{document}</tex-math></inline-formula> with no non-trivial rational characters. Our results rely on (1) a non-divergent criterion on <inline-formula><tex-math id=M16>begin{document}$ {text{SL}}_n $end{document}</tex-math></inline-formula> proved by geometry of numbers and a theorem of Kleinbock–Margulis; (2) relations between partial Borel–Serre compactifications associated with different groups proved by geometric invariant theory and reduction theory. <b>193</b> words.</p>" @default.
• W3217791106 created "2021-12-06" @default.
• W3217791106 creator A5083154414 @default.
• W3217791106 date "2022-01-01" @default.
• W3217791106 modified "2023-09-25" @default.
• W3217791106 title "Equidistribution of translates of a homogeneous measure on the Borel–Serre compactification" @default.
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• W3217791106 doi "https://doi.org/10.3934/dcds.2021183" @default.
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